Question

A true/false test has ? = 20 questions. If a student is simply guessing the answers

(so there is a 50% chance of getting correct for each question),

a) what is the mean and standard deviation of the number of questions the student would get

correct?

Mean = ______, Standard deviation = ______

b) what is the approximate probability (approximated by a normal distribution) that this student would get at least 15 questions correct?

P (at least 15 questions correct) = ___________.

c) what is the approximate probability (approximated by a normal distribution) that this student would get no more than 10 questions correct?

P (no more than 10 questions correct) = ______.

d) what is the approximate probability (approximated by a normal distribution) that this student would get no more than 12 questions correct?

P (no more than 12 questions correct) = ______.

e) what is the approximate probability (approximated by a normal distribution) that this student would get more than 8 but less than 12 questions correct?

P (get more than 8 but less than 12 questions correct) = __________.

Answer 1

Let X be the number of question correctly answered .

Let X_i = 1 if i ^th question is answered corectly , with probability p=0.5

= 0 , if answered wrongfully.

So,   

a) So, mean = E(X) = 20 * 0.5 = 10

variance = var(X) = 20*0.5*0.5 = 5

so, standard deviation = 2.24

b) By CLT

  

  

  

c)

d)

e)

=

If you have doubts, let me know below . Thanks